At home you are most likely behind a home router, so the Internet cannot see your Mac. Only the other devices in your home.
At a public WiFi they are generally behind a router as well, so it will ONLY be the other people sharing the router. And I've found that for a lot of those, they actually isolate each connection from the other (but that will not be 100%). That is to say, when I've tried to sniff for other users, I've only seen myself, even though there are others using their devices.
My point is that it is not going to be the entire Internet you are protecting yourself from with Stealth mode.
The only way your Mac would be visible is if you do NOT use a home router and connect your Mac directly to your Internet Service Provider's network connection (no router, and the ISP does not provide a router).
And totally invisible is impossible, as once you make a connection you are telling the other party where you are.
If and ONLY IF the public WiFi is NOT isolating each customer, other users would be able to sniff your traffic and see that you are there. No need to send a probe to a random IP address and hope it responds to detect if you are at that IP address, they can just read your network packets and see your IP address. Then they can target well known ports to see if you have them open. And then once they know what ports you have open, they can try to break in by guessing the necessary access codes (username/passwords, etc...).
NOTE: guessing your username and password is not trivial, especially if you use a good password, and your username is not 'root'.
If you are worried about public WiFi access, then use a VPN service and have all your network traffic go over an encrypted link to the VPN server and then it will be decrypted and put on the Internet. Hopefully no three letter agency is capturing the output from the VPN provider's servers as they enter the internet. Of course you could install a VPN server on a home system, and connect to that. Your VPN server at home would then decrypt your VPN traffic and put it on the internet just like you would if you are at home (NOTE: your surf'ing speed would be limited to the speed of your home ISP up-load speed, as you pull web pages in at home, encrypted them, and up-load them over the VPN to wherever your Mac is sitting on a public WiFi; home up-load speeds are often much slower than the download speeds).
The best counter measure on a Mac is that stuff between your ears. So far the biggest Mac threat is Adware and Phishing attacks. The Adware requires you to be tricked into downloading and installing it. The Phishing attacks, generally send an email, or have a web page pop-up that makes you think it is an official request for you to call the 1-800 number and get credit card, or access to information from you, or make you think you should login with your Apple ID, or PayPal account, etc... via the web link they provide. In other words, they get you do to give up the information.
You should read
How does Mac OS X protect me?